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In this study, semi-analytical solutions are presented for the time periodic (electroosmotic flow) of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the nonlinear Poisson-Boltzmann (P-B) equation, the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of the dimensionless wall Zeta potential0, the periodic EOF electric oscillating Reynolds number Re, and normalized relaxation times 1 on velocity profiles are presented. Results show that for prescribed electrokinetic width K, relaxation time 1 and oscillating Reynolds number Re, higher Zeta potential 0 will lead to larger amplitude of EOF velocity, and the variation of velocity is restricted to a very narrow region close to the Electric double-layer. In addition, with the increase of relaxation time 1, the elasticity of the fluid becomes conspicuous and the velocity variations can be expanded to the whole flow field. For prescribed Re, longer relaxation time 1 will lead to quick change of the EOF velocity profile, and the amplitude becomes larger gradually.
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Keywords:
- EDL /
- time periodic EOF /
- generalized Maxwell fluids /
- micro-parallel plates
[1] Stone H A, Stroock A D, Ajdari A 2004 Ann. Rev. Fluid Mech. 36 381
[2] Bayraktar T, Pidugu S B 2006 Int. J. Heat Mass Transfer 49 815
[3] Burgreen D, Nakache F R 1964 J. Phys. Chem. 68 1084
[4] Levine S, Marriott J R, Neale G, Epstein N 1975 J. Colloid Interface Sci. 52 136
[5] Tsao H K 2000 J. Colloid Interface Sci. 225 247
[6] Kang Y J, Yang C, Huang X Y 2002 J. Colloid Interface Sci. 253 285
[7] Hsu J P, Kao C Y, Tseng S J, Chen C J 2002 J. Colloid Interface Sci. 248 176
[8] Yang C, Li D, Masliyah J H 1998 Int. J. Heat Mass Transfer 41 4229
[9] Arulanandam S, Li D 2000 Colloids Surf. A: Physicochem. Eng. Aspects 161 89
[10] Bianchi F, Ferrigno R, Girault H H 2000 Anal. Chem. 72 1987
[11] Wang C Y, Liu Y H, Chang C C 2008 Phys. Fluids 20 063105
[12] Dutta P, Beskok A 2001 Anal. Chem. 73 5097
[13] Keh H J, Tseng H C 2001 J. Colloid Interface Sci. 242 450
[14] Kang Y J, Yang C, Huang X Y 2002 Int. J. Eng. Sci. 40 2203
[15] Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101
[16] Chakraborty S, Ray S 2008 Phys. Fluids 20 083602
[17] Chakraborty S, Srivastava A K 2007 Langmuir 23 12421
[18] Qu W L, Li D Q 2000 J. Colloid Interface Sci. 224 397
[19] Jian Y J, Yang L G, Liu Q S 2010 Phys. Fluids 22 042001
[20] Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15
[21] Chakraborty S 2007 Anal. Chim. Acta 605 175
[22] Zhao C, Zholkovskij E, Masliyah J H, Yang C 2008 J. Colloid Interface Sci. 326 503
[23] Vasu N, De S 2010 Colloids and Surfaces A: Physicochem. Eng. Aspects 368 44
[24] Zhao C, Yang C 2010 Electrophoresis 31 973
[25] Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian fluid Mech. 157 133
[26] Wang R J, Lin J Z, Li Z H 2005 Binmedical Microdevices 7 131
[27] Zhang K, Lin J Z, Li Z H 2006 Appl. Math. Mech. ( English Edition) 27 575
[28] Lin J Z, Zhang K, Li H J 2006 Chin. Phys. 15 2688
[29] Liu Q S, Jian Y J, Yang L G 2011 J. Non-Newtonian fluid Mech. 166 478
[30] Jian Y J, Liu Q S, Yang L G 2011 J. Non-Newtonian fluid Mech. 166 1304
[31] Jian Y J, Liu Q S, Duan H Z, Chang L, Yang L G 2011 The Sixth International Conference on Fluid Mechanics (ICFM6), Guang Zhou, June 30-July 3, p616
[32] Bird R B, Stewart W E, Lightfoot E N 2001 Transport phenomena, Second Edition (New York: Wiley-Interscience Publication) p242
[33] Gong L, Wu J, Wang L, Cao K 2008 Phys. Fluids 20 063603
[34] Goswami P, Chakraborty S 2009 Langmuir 26 581
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[1] Stone H A, Stroock A D, Ajdari A 2004 Ann. Rev. Fluid Mech. 36 381
[2] Bayraktar T, Pidugu S B 2006 Int. J. Heat Mass Transfer 49 815
[3] Burgreen D, Nakache F R 1964 J. Phys. Chem. 68 1084
[4] Levine S, Marriott J R, Neale G, Epstein N 1975 J. Colloid Interface Sci. 52 136
[5] Tsao H K 2000 J. Colloid Interface Sci. 225 247
[6] Kang Y J, Yang C, Huang X Y 2002 J. Colloid Interface Sci. 253 285
[7] Hsu J P, Kao C Y, Tseng S J, Chen C J 2002 J. Colloid Interface Sci. 248 176
[8] Yang C, Li D, Masliyah J H 1998 Int. J. Heat Mass Transfer 41 4229
[9] Arulanandam S, Li D 2000 Colloids Surf. A: Physicochem. Eng. Aspects 161 89
[10] Bianchi F, Ferrigno R, Girault H H 2000 Anal. Chem. 72 1987
[11] Wang C Y, Liu Y H, Chang C C 2008 Phys. Fluids 20 063105
[12] Dutta P, Beskok A 2001 Anal. Chem. 73 5097
[13] Keh H J, Tseng H C 2001 J. Colloid Interface Sci. 242 450
[14] Kang Y J, Yang C, Huang X Y 2002 Int. J. Eng. Sci. 40 2203
[15] Wang X M, Chen B, Wu J K 2007 Phys. Fluids 19 127101
[16] Chakraborty S, Ray S 2008 Phys. Fluids 20 083602
[17] Chakraborty S, Srivastava A K 2007 Langmuir 23 12421
[18] Qu W L, Li D Q 2000 J. Colloid Interface Sci. 224 397
[19] Jian Y J, Yang L G, Liu Q S 2010 Phys. Fluids 22 042001
[20] Das S, Chakraborty S 2006 Anal. Chim. Acta 559 15
[21] Chakraborty S 2007 Anal. Chim. Acta 605 175
[22] Zhao C, Zholkovskij E, Masliyah J H, Yang C 2008 J. Colloid Interface Sci. 326 503
[23] Vasu N, De S 2010 Colloids and Surfaces A: Physicochem. Eng. Aspects 368 44
[24] Zhao C, Yang C 2010 Electrophoresis 31 973
[25] Tang G H, Li X F, He Y L, Tao W Q 2009 J. Non-Newtonian fluid Mech. 157 133
[26] Wang R J, Lin J Z, Li Z H 2005 Binmedical Microdevices 7 131
[27] Zhang K, Lin J Z, Li Z H 2006 Appl. Math. Mech. ( English Edition) 27 575
[28] Lin J Z, Zhang K, Li H J 2006 Chin. Phys. 15 2688
[29] Liu Q S, Jian Y J, Yang L G 2011 J. Non-Newtonian fluid Mech. 166 478
[30] Jian Y J, Liu Q S, Yang L G 2011 J. Non-Newtonian fluid Mech. 166 1304
[31] Jian Y J, Liu Q S, Duan H Z, Chang L, Yang L G 2011 The Sixth International Conference on Fluid Mechanics (ICFM6), Guang Zhou, June 30-July 3, p616
[32] Bird R B, Stewart W E, Lightfoot E N 2001 Transport phenomena, Second Edition (New York: Wiley-Interscience Publication) p242
[33] Gong L, Wu J, Wang L, Cao K 2008 Phys. Fluids 20 063603
[34] Goswami P, Chakraborty S 2009 Langmuir 26 581
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